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If one assumes the validity of conventional quantum field theory in thevicinity of the horizon of a black hole, one does not find a quantum mechanicaldescription of the entire black hole that even remotely resembles that ofconventional forms of matter; in contrast with matter made out of ordinaryparticles one finds that, even if embedded in a finite volume, a black holewould be predicted to have a strictly continuous spectrum.  Dissatisfied with such a result, which indeed hinges on assumptionsconcerning the horizon that may well be wrong, various investigators have nowtried to formulate alternative approaches to the problem of ``quantizing" theblack hole. We here review the approach based on the assumption of quantummechanical purity and unitarity as a starting point, as has been advocated bythe present author for some time, concentrating on the physics of the statesthat should live on a black hole horizon. The approach is shown to be powerfulin not only producing promising models for the quantum black hole, but also newinsights concerning the dynamics of physical degrees of freedom in ordinaryflat space-time.Comment: Review paper, 71 pages plain TEX, 8 Figures (Postscript

THE SCATTERING MATRIX APPROACH FOR THE QUANTUM BLACK HOLE: AN OVERVIEW